Necklace Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =10a(5) =34a(6) =116a(7) =396a(8) =1353a(9) =4631a(10) =15895a(11) =54757a(12) =189465a(13) =658835a(14) =2303381a(15) =8098783a(16) =28642314a(17) =101894922a(18) =364614216a(19) =1312191768a(20) =4748561094a(21) =17275277322a(22) =63163858146a(23) =232041604038a(24) =856219298484